Fixing S-trap under kitchen sink

I live in an old house and the plumbing is not up-to-code. Every single sink in my house has an S-trap. The easiest one to fix is the kitchen sink and I am trying to figure out the best way to go about doing so.

The old configuration was a mess (the garbage disposal did not drain well- and got to the point that I had to reach my hand in and push stuff around to get it to drain-- the disposal itself would no longer turn and was rusted):

Because it was already S-trapped and there was no available outlet through the wall for a vent (and I needed to get this fixed asap since the sink had been out of commission and dishes were piled up), I'm temporarily using this setup:

I then started thinking of how to configure it so that I could get it vented properly (AAVs are NOT allowed in my state so that option was out). I came up with this crappy rough sketch.

After looking up some parts I started to get a better idea of what I could do. I figured I could use a compression to PVC fitting to bridge it to a 1 1/2" sanitary tee that takes it down to 1 1/2" to 3" (or 2" if it turns out that is the pipe size under the house) wye to hook up to the existing pipe that has a cleanout and on top of the tee I would have an elbow to take the pipe out through the wall at an angle (so it would not be a flat vent) and another elbow to make it go up outside the exterior of the wall.
(obviously that is not to scale)

My next hurdle is the window above the sink. As you can see in this photo, the existing vent pipe routes around the window. I'm not sure if it is actually 6 inches above the flood level and this terminates under the soffit.

Currently the sink drains to a pipe under the house and then comes out from under the house (flat vent) and then back up along the exterior wall. I know that isn't to code. So, once outside the house I would need to route it around without having it go flat/horizontal before the 6" mark. I'm thinking another elbow or something and trying to get it to start going sideways at an earlier point with another elbow. I'm just not sure how to measure for the angles and where all of the holes should be. I am not thrilled with drilling through the siding, but I don't want to tear up the backsplash above the sink. (I don't care about the look under the sink).

Your pipe through the wall connect to low to be correct the way you show it. From your drawing, if correct, and since you have to make a hole in the wall anyway, why not just insert a T at the proper height and connect the "P" trap to it?

Wait, connects too low to where?
I'm not sure what the proper height is...
Is the part where it goes down in to the floor starting off too low?
This is one of the things I'm confused about and I didn't see the reference in the plumbing code (but then my state has a very long plumbing code)
I tend to do better with visuals. Do you have any pictures? (Sorry to be a pain)

When I was a kid, there were a lot of houses built without indoor plumbing still around. What HJ is describing as the solution to plumbing your kitchen sink is what people were doing maybe 80 years ago to retrofit plumbing to an existing house.
The vent pipe would come out from under the house( right by those two sleeping hound dogs), and 90 up the wall to a tee which catches the kitchen sink on it's way up the outside wall.
Good luck on the interior fixtures. I wouldn't dare suggest civil disobedience in regards to AAVs in the bathroom.

When you make a connection to an existing vent line, it must be made at least 42" above the floor OR 6" above the flood plane of the fixture it is venting whichever is higher. That's what HJ is talking about in height.

Now, this assumes you're keeping the existing vent line that comes from below. Without knowing what is down there that that line is actually venting, no idea if it is a valid vent line at all. Termination beneath the eaves is not a good idea, either!

fullysprinklered, you're describing what is pretty much the current vent pipe situation except that there is an S trap and the pipe just goes down under the house. The house is raised off the ground 2.5' to 3' (I think, I haven't really measured-- it could be more).

hj, Hmmm. Do you happen to know the code off hand? I didn't see anything when I looked at my state's plumbing code. I found a reference online to the forty-two inch rule for yoke vents in an Idaho code book (907.2), but there was no occurrence of anything being 42 inches in the Louisiana Plumbing code.

In the Idaho code book it said907.2 The yoke vent connection to the vent stack shall be placed not less than forty-two (42) inches (1,067 mm) above the floor level, and the yoke vent connection to the drainage stack shall be by means of a wye-branch fitting placed below the lowest drainage branch connection serving that floor.

In the Louisiana code a yoke vent is defined on page 311.Yoke Vent—a pipe connecting upward from a soil or waste stack to a vent stack for the purpose of preventing pressure changes in the stacks.

I don't know if it matters, but my kitchen sink is the only fixture on that vent and probably the only one on that branch of the drain (I'm not sure how it ties in to the main soil pipe because its hard to get in a spot to see clearly).

I just re-read through the section on venting and I also did a search for any reference to 42-inch (and the number 42) and there is nothing about the height, not even for yoke vents.

Here are two snippets I screencapped

What is a short turn quarter bend?

Oops, I started this before the post from jadnashua. To clarify: the kitchen sink is the only fixture on this vent and basically they just S trapped the sink and ran it down to connect to the waste pipe (which then somehow connects to the main soil pipe-- I hope). I don't know what the original venting system was, but when we came back from overseas the plumber looked and said that the tenants had ripped out all of the plumbing vents (he had been the original plumber for the house so he would probably know how things were done like 40 years before or whenever he did the stuff).
Right now the pipe comes out from under the house and has a cleanout, but just before the cleanout is a vent pipe that goes up underneath the window, 90 elbow to the south, then 90 elbow back up again, then terminates under the soffit. I don't know if it was that he didn't finish or if the siding people cut it off accidentally or what. On another side of the house he has an elbow under the soffit that takes it out from under the soffit and then an elbow back up to vent above the roof.

I thought that the 6" rule applied to horizontal runs and I'm trying to use fittings that will make the pipe run as vertically as possible but still exit through the wall. Am I missing something? (I hope this doesn't seem combative, I really am curious)

Here is a pic of how the pipe comes out from under the house from the kitchen sink:

Here is it terminating under the soffit:

Here is the vent on the other side of the house. It seems to be the one that serves two bathrooms (at least I hope the fixtures in the other bathroom are hooked up to it-- it seems like two bathroom groups are probably wet-vented together, but I'll have to go look at the plumbing under there).

I plan to eliminate the part of the pipe that is lower down and connects just before the cleanout and continue on upward from the part coming out of the wall.

Note to self: looks like its a 2" pipe and vent for the kitchen sink when I compare it to the size of the other pipe which I believe is 3".
The inside window sill is about 6.5" above the top rim of the sink and the sink does not seem to have anything to stop overflow, so I think that the existing horizontal run under the window is not right.

The 6" above the fixture overflow level, OR 42" above the floor, whichever is HIGHER, is a requirement in EVERY code, you just haven't found it. A 'yoke vent" is usually IMPOSSIBLE to install at 42" because it is usually under the sink which is only 36" high.

Another thought: What if I eliminate the downward pipe underneath the cabinet that goes down through the floor and just have it go out through the wall to vent and just use a sanitary tee. I live in an area where it doesn't usually get below 20 degrees even in the coldest winters. While it has snowed the past couple of years, it is a rare occurrence. I know that the cold is more of a concern for inside of the trap and any water supply lines though. Hot water from the sink would probably melt any ice.